Sharp interfaces

Figure 5 Images of a thin region of an epitaxial film of Ge on Si grown by oxidation of Ge-implanted Si (a) conventional TEM phase contrast image with no compositional information and b) high-angle dark-field STEM image showing atomically sharp interface between Si and Ge. (Courtesy of S.J. Pennycook)...

In numerous applications of polymeric materials multilayers of films are used. This practice is found in microelectronic, aeronautical, and biomedical applications to name a few. Developing good adhesion between these layers requires interdiffusion of the molecules at the interfaces between the layers over size scales comparable to the molecular diameter (tens of nm). In addition, these interfaces are buried within the specimen. Aside from this practical aspect, interdififlision over short distances holds the key for critically evaluating current theories of polymer difllision. Theories of polymer interdiffusion predict specific shapes for the concentration profile of segments across the interface as a function of time. Interdiffiision studies on bilayered specimen comprised of a layer of polystyrene (PS) on a layer of perdeuterated (PS) d-PS, can be used as a model system that will capture the fundamental physics of the problem. Initially, the bilayer will have a sharp interface, which upon annealing will broaden with time. 

Neutron reflectivity is ideally suited to this problem, since concentration profiles can be resolved on the nanometer level and since, for an infinitely sharp interface, Rkjf will approach asymptotically a constant value. In addition, neutron reflectivity is nondestructive and multiple experiments can be performed on the same specimen. Figure 4 shows a plot of Rk Q as a function of bilayer of protonated... 

Figure 4 The reflectivity multiplied by kjQ as a function of for a bilayer of normal polystyrene on perdautarated polystyrene before and after heating at 105.5° C for 2 minutes. The data is plotted in this manner since for sharp interfaces RkjQ is a constant at large k -...

These apparent restrictions in size and length of simulation time of the fully quantum-mechanical methods or molecular-dynamics methods with continuous degrees of freedom in real space are the basic reason why the direct simulation of lattice models of the Ising type or of solid-on-solid type is still the most popular technique to simulate crystal growth processes. Consequently, a substantial part of this article will deal with scientific problems on those time and length scales which are simultaneously accessible by the experimental STM methods on one hand and by Monte Carlo lattice simulations on the other hand. Even these methods, however, are too microscopic to incorporate the boundary conditions from the laboratory set-up into the models in a reahstic way. Therefore one uses phenomenological models of the phase-field or sharp-interface type, and finally even finite-element methods, to treat the diffusion transport and hydrodynamic convections which control a reahstic crystal growth process from the melt on an industrial scale. 

M. Benes. On a computational comparison of phase-field and sharp-interface model of microstructure growth in solidification. Acta Technica CSAV 41 591,... 

The Alexander approach can also be applied to discover useful information in melts, such as the block copolymer microphases of Fig. 1D. In this situation the density of chains tethered to the interface is not arbitrary but is dictated by the equilibrium condition of the self-assembly process. In a melt, the chains must fill space at constant density within a single microphase and, in the case of block copolymers, minimize contacts between unlike monomers. A sharp interface results in this limit. The interaction energy per chain can then be related to the energy of this interface and written rather simply as Fin, = ykT(N/Lg), where ykT is the interfacial energy per unit area, q is the number density of chain segments and the term in parentheses is the reciprocal of the number of chains per unit area [49, 50]. The total energy per chain is then ... 

AB diblock copolymers in the presence of a selective surface can form an adsorbed layer, which is a planar form of aggregation or self-assembly. This is very useful in the manipulation of the surface properties of solid surfaces, especially those that are employed in liquid media. Several situations have been studied both theoretically and experimentally, among them the case of a selective surface but a nonselective solvent [75] which results in swelling of both the anchor and the buoy layers. However, we concentrate on the situation most closely related to the micelle conditions just discussed, namely, adsorption from a selective solvent. Our theoretical discussion is adapted and abbreviated from that of Marques et al. [76], who considered many features not discussed here. They began their analysis from the grand canonical free energy of a block copolymer layer in equilibrium with a reservoir containing soluble block copolymer at chemical potential peK. They also considered the possible effects of micellization in solution on the adsorption process [61]. We assume in this presentation that the anchor layer is in a solvent-free, melt state above Tg. The anchor layer is assumed to be thin and smooth, with a sharp interface between it and the solvent swollen buoy layer. 

Fig. 5. Hydrogen depth profile of a deuterated polystyrene PS(D) film deposited on a protonated polystyrene PS(H) film on top of a silicon wafer as obtained by l5N-nuclear reaction analysis ( 5N-NRA). The small hydrogen peak at the surface is due to contamination (probably water) of the surface. The sharp interface between PS(D) and PS(H) is smeared by the experimental resolution (approx. 10 nm at a depth of 80 nm) [57], The solid line is a guide for the eye...

Morphology of the anionically synthesized triblock copolymers of polyfp-methyl-styrene) and PDMS and their derivatives obtained by the selective chlorination of the hard segments were investigated by TEM 146). Samples with low PDMS content (12%) showed spherical domains of PDMS in a poly(p-methylstyrene) matrix. Samples with nearly equimolar composition showed a continuous lamellar morphology. In both cases the domain structure was very fine, indicating sharp interfaces. Domain sizes were estimated to be of the order of 50-300 A. 

Two requirements should be satisfied in order to achieve the enhancement in strength of the superlattices modulation wavelength (X.) in the scale of nanometre and sharp interfaces between layers. There is an optimum for a superlattice film to achieve the maximum strength, as shown in Fig. 12 [100-102]. The strength of the superlattice film will de-... 

The interfaces here also have contribution to the hardness. For Samples 3 and 4, there are no obvious interfaces between Layers A and B because the individual layer thickness is so thin that it is hard to form sharp interfaces. It is more like a mixed structure according to the process. For Sample 5, the interfaces are possibly formed due to the increase of Layer A. So the hardness of Samples 3 and 4 is still much lower than monolayer A, but the hardness of Sample 5 is close to the monolayer A. 

Among interface capturing methods, one of the most popular and most successful schemes is the volume-of-fluid (VOF) method dating back to the work of Hirt and Nichols [174]. The VOF method is based on a volume-fraction field c, assuming values between 0 and 1. A value of c = 1 indicates cells that are filled with phase 1, and phase 2 corresponds to c= 0. Intermediate values of c indicate the position of the interface between the phases however, the goal is to maintain a sharp interface in order to identify the different fluid phases uniquely. Volumes assigned to the different phases are moving with the local flow velocity W , and therefore the evolution of c is determined by a convection equation ... 

A simple method used to maintain a sharp interface is based on a correction algorithm [175]. After each time step, the amount of fluid of a specific phase having penetrated the interface at c = 0.5 is determined. Then the fluid is redistributed such that the voids on the other side of the interface are filled up. The redistribution is done globally, as information on the origin of fluid volumes having pen-... 

In addition to the methods described above, there exist a number of other methods for the computation of free-surface flows which allow a sharp interface to be maintained. The approach which resembles computational methods for single-... 

By using a multichamber system [129], exchange of residual gases between successive depositions will be strongly decreased, and very sharp interfaces can be made. Furthermore, the use of a load-lock system ensures high quality of the background vacuum, and thus low levels of contaminants in the bulk layers. Multichamber reactor systems have been used for the fabrication of solar cells, and considerable improvements in energy conversion efficiency have been achieved [130, 131]. 

When a monolayer of phospholipids is adsorbed at the ITIES, there must be a modification of the electrical structure of the interface [60]. Since we aim at describing the effect of this monolayer on the rate of ion transfer in a simple way, we assume a sharp interface also in the presence of phospholipids. The hydrophobic tails are located in the organic phase (negative x region), and the hydrophilic headgroups are located in the aqueous phase (positive X region). 

Strictly speaking, the validity of the shrinking unreacted core model is limited to those fluid-solid reactions where the reactant solid is nonporous and the reaction occurs at a well-defined, sharp reaction interface. Because of the simplicity of the model it is tempting to attempt to apply it to reactions involving porous solids also, but this can lead to incorrect analyses of experimental data. In a porous solid the chemical reaction occurs over a diffuse zone rather than at a sharp interface, and the model can be made use of only in the case of diffusion-controlled reactions. 

The fundamental physical properties of nanowire materials can be improved even more to surpass their bulk counterpart using precisely engineered NW heterostructures. It has been recently demonstrated that Si/Ge/Si core/shell nanowires exhibit electron mobility surpassing that of state-of-the-art technology.46 Group III-V nitride core/shell NWs of multiple layers of epitaxial structures with atomically sharp interfaces have also been demonstrated with well-controlled and tunable optical and electronic properties.47,48 Together, the studies demonstrate that semiconductor nanowires represent one of the best-defined nanoscale building block classes, with well-controlled chemical composition, physical size, and superior electronic/optical properties, and therefore, that they are ideally suited for assembly of more complex functional systems. 

A binary suspension consists of equal masses of spherical particles of the same shape and density whose free falling velocities in the liquid are 1 mm/s and 2 mm/s, respectively. The system is initially well mixed and the total volumetric concentration of solids is 0.2. As sedimentation proceeds, a sharp interface forms between the clear liquid and suspension consisting only of small particles, and a second interface separates the suspension of fines from the mixed suspension. Using a suitable model for the behaviour of the system, estimate the falling rates of the two interfaces. It may be assumed that the sedimentation velocity uc in a concentrated suspension of voidage e is related to the free falling velocity u0 of the particles by ... 

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